(i) Field of the Invention
The invention relates to a device for individual in-vivo determination of the compliance function C()=dV/dp of the vascular system downstream of a ventricle of a living being from the blood pressure p(t) and a reference cardiac output COref.
The invention also relates to a device for continuously determining the systemic blood flow q(t), in which the blood pressure p(t) in the aorta or in the vicinity of the aorta is determined continuously.
(ii) Description of Related Art
Methods and devices of the type mentioned above are known. In the past, a plurality of methods have been developed with the purpose of calculating the cardiac output (CO) from the arterial blood pressure. On the one hand, methods are proposed in which the CO is determined from a few characteristic values such as, for example, mean arterial pressure (MP), systolic and diastolic pressure (APsys, APdia), ejection time (ET) and patient data (age, sex, weight, height) [4,6,7], and on the other hand algorithms are used in which the complete contour of the pulsating blood pressure curve is utilized to calculate the cardiac output [1,5,20]. In the latter methods, which are also referred to as pulse contour analysis, two different approaches have so far been adopted. Firstly, the CO has been calculated directly from the arterial blood pressure with the aid of some correction factors [19,20] while in other work [5,25] a blood flow is calculated from the pressure, together with particular assumptions, and is assumed to correspond to the actual blood flow in the aorta and therefore to be usable for determining the cardiac output.
The classical Windkessel model, which was first proposed by Hales [26] and has been used by Frank [27] to determine the stroke volume (SV) and, together with the heart rate, the cardiac output, uses only the peripheral resistance R and the compliance C for modeling the cardiovascular system in question. In this model, the arterial blood flow is described by q(t), which can be calculated for given C and R with the aid of the blood pressure p(t) which is to be measured. However, closer examination shows that this simple model reproduces the physiological conditions only incompletely, with the result that many modifications to the original model have been proposed; for an overview reference may be made to [24,28].
The accuracy of these methods depends essentially on how well the assumptions, i.e. the model used, reflect the conditions in the cardiovascular system in question, and in [5] a nonlinear Windkessel model is thus used whose parameters are dictated by the age and sex of the patient. More recent investigations [21] show, however, that the model used in [5] does not reproduce the correct underlying physiological conditions; in particular the compliance (extensibility) of the vessels cannot always be described by the compliance/pressure relationship given in [5]. There may be several causes for this discrepancy. First, only a dependence of the in-vitro determined aortic cross section on the blood pressure is taken into account in [5] and a length variation, as described in [22,23] is neglected; also, only the density of the blood and not the strongly hematocrit-dependent viscosity is taken into account, and the compliance of the peripheral system is likewise ignored. Secondly, apart from age and sex, the compliance function C(p) of a particular individual cannot be used in the method described in [5]. However, it is precisely in the examination of pathophysiological cases, e.g. arteriosclerosis, that it cannot be assumed that C(p) varies according to age and sex, so that the basic model describes the physiological conditions only incompletely [25]. Lastly, it has been shown in [24] that it is to be expected that a modified Windkessel model can reproduce underlying physiological conditions more precisely.
However, a common factor in all the models described above is that the model parameters, after they have been determined once, no longer depend on the condition of the cardiovascular system in question. Nevertheless, almost all parameters can change with time, and for example the systemic resistance R can change as a result of medication. Other parameters, including the expandability and length of the aorta, change so greatly with pressure that they actually have to be regarded as variable even within one heartbeat.
The fact that aortic impedance and compliance cannot be assumed to be constant has been shown both in animal experiments [22] and for humans [29]. Primary causes of this are the expandability, length variation and volume variation of the aorta and vessels in proximity to the aorta. The typical variation in the aortic volume V as a function of pressure has been described inter alia in [30]. Since the compliance of the system is given by ##EQU2##
and because of the limited volume the compliance must tend toward zero for very high pressures and cannot be constant. Since the change in volume is caused by length and cross-sectional changes in the vessels, there is also a change in the aortic impedance which, according to the Navier-Stokes equation, is determined on the one hand by the cross section and density of the liquid and, on the other hand, by length, viscosity and density of the blood.
Pressure-dependent aortic impedance and compliance have been discussed inter alia in [5,21] and used therein to investigate nonlinear Windkessel models. In [5] it is in particular assumed that C(p) can be established by age and sex of the patient. The impedance Z(p) is also ignored in this approach. What is more, it follows from the results obtained in [21] that the model used in [5] may to some extent conflict with the true physiological situation. One cause of this is that the compliance and aortic impedance are preset. An approach of this type is unsuitable for taking into account the features characteristic of the patient in question. In addition, the method proposed in [5] cannot be applied without modifications to other species. Further, only the typical aortic diameter investigated beforehand in-vitro and the density of the blood are taken into account in [5]. The effect of aortic length variations, and the dynamic behavior of the vessels in proximity to the aorta and the peripheral vessels and the viscosity of the blood are ignored in the modeling of the conditions existing in vivo.
There is consequently not yet any method which, for individual in-vivo determination of the compliance/pressure relationship, employs the measured variables used here.
These disadvantages are to be eliminated by the device of the present invention by determining all model parameters of interest from measurements on the physiological system in question, i.e. human or animal. To this end, in particular, the blood pressure p(t) in the aorta or in proximity to the aorta is to be measured continuously and a reference cardiac output (COref) is to be measured at least one time. With the aid of these values, all the parameters can be established and then used for hemodynamic investigation.